The resonance behavior in two coupled harmonic oscillators with fluctuating mass

Yu, Tao; Zhang, Lu; Zhong, Shun; Li, Lai

doi:10.1007/s11071-019-04881-2

Cited by 19 publications

(11 citation statements)

References 43 publications

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“…Based on the stationary response theory [21][22][23][24], the harmonic oscillator driven by a periodic signal has stationary periodic output at the driving frequency. As a linear system in equation ( 1) driven by multiple periodic signals with frequencies f n ±kf d , the stationary output can be written as the sum of multiple periodic components at the corresponding frequencies, indicating that only the periodic components 5) have the possibility to produce a stationary periodic response at the bearing fault frequency f d , i.e.…”

Section: Ffamentioning

confidence: 99%

“…Herein, we can analyze the system stationary state response under the framework of the classical method proposed in [24,[29][30][31].…”

Section: Ffamentioning

confidence: 99%

“…Recently, as the SR-like phenomenon was found in the linear oscillator (LO) with multiplicative fluctuation [19,20], the concept of SR was extended to generalized SR (GSR), which meant the non-monotonic phenomena of output function, such as moments, autocorrelation functions and SNR, varied with the system parameters [21][22][23][24]. It is well known that the linear system has a lower computational cost in the numerical implementation.…”

Section: Introductionmentioning

confidence: 99%

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A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

Zhang¹,

Chen²,

Wang³

2023

Meas. Sci. Technol.

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Stochastic resonance (SR) has been widely used in bearing fault diagnosis due to the enhancement principle of energy conversion from noise to weak signal. However, the diagnosis efficiency and robustness is still challenging.Under the mechanism of generalized stochastic resonance (GSR), in the paper we propose a scale-transformed linear oscillator (SLO), and obtain the analytical expression of fault feature amplification (FFA) to replace the numerical implementation of output signal-to-noise ratio (SNR) in the multi-parameter optimization.It brings the substantial benefit to the reduction of time complexity in fast fault diagnosis, which is verified in both theory and simulations.In the experimental diagnosis for some typical cases, the results show that the proposed method is valid and exhibits the superiority in diagnosis performance, efficiency, and robustness, which demonstrates that the FFA-guided GSR-SLO method has great potential in the engineering applications, especially the real-time fault diagnosis in complex operating environments.

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Section: Ffamentioning

confidence: 99%

“…Herein, we can analyze the system stationary state response under the framework of the classical method proposed in [24,[29][30][31].…”

Section: Ffamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

Zhang¹,

Chen²,

Wang³

2023

Meas. Sci. Technol.

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“…由于方程(1)在波动障碍穿越 [36] 、酶动力学 [37] 及核磁共振 [38] 等化学、生物、物理多个领域存在应用, 所以关于这类模型的研究具有较高的理论和应用价值. 文献 [25,39] 关系还会丰富系统的共振行为 [19][20][21][22][23]28,40,41] . Pikovsky 等 [22] 发现不同类型的耦合随机系统中都存在系统规模共振.…”

Section: 近期研究成果表明在乘性噪声驱动下的线性系统unclassified

Collective behaviors of globally coupled harmonic oscillators driven by different frequency fluctuations

Jiang¹,

Li²,

Yu³

et al. 2021

Acta Phys. Sin.

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For multi-particle coupled systems, the effects of environmental fluctuations on each particle are often different in actual situations. To this end, this paper studies the collective dynamic behaviors in globally coupled harmonic oscillators driven by different frequency fluctuations, including synchronization, stability and stochastic resonance (SR). The statistical synchronicity between particles' behaviors is derived by reasonably grouping variables and using random average method, and then the statistical equivalence between behaviors of mean field and behaviors of single particle is obtained. Therefore, the characteristics of mean field's behaviors (that is, collective behaviors) can be obtained by studying behaviors of any single particle. Moreover, the output amplitude gain and the necessary and sufficient condition for the system stability are obtained by using this synchronization. The former lays a theoretical foundation for analyzing the stochastic resonance behavior of the system, and the latter gives the scope of adaptation of the conclusions in this paper. In terms of numerical simulation, the research is mainly carried out through the stochastic Taylor expansion algorithm. Firstly, the influence of system size N and coupling strength <inline-formula><tex-math id="M3">\begin{document}$\varepsilon$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M3.png"/></alternatives></inline-formula> on the stability area and synchronization time is analyzed. The results show that with the increase of the coupling strength <inline-formula><tex-math id="M4">\begin{document}$\varepsilon$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M4.png"/></alternatives></inline-formula> or the increase of the system size N, the coupling force between particles increases, and the orderliness of the system increases, so that the stable region gradually increases and the synchronization time gradually decreases. Secondly, the stochastic resonance behavior of the system is studied. Noises provide randomness for the system, and coupling forces provide orderliness for the system. The two compete with each other, so that the system outputs about the noise intensity <inline-formula><tex-math id="M5">\begin{document}$\sigma$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M5.png"/></alternatives></inline-formula>, the coupling strength <inline-formula><tex-math id="M6">\begin{document}$\varepsilon$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M6.png"/></alternatives></inline-formula> and the system size N exhibit stochastic resonance behavior. As the coupling strength increases or the system size increases, the orderliness of the system increases, and greater noise intensity is required to provide stronger randomness to achieve optimal matching with it, so as to the resonance of the noise intensity <inline-formula><tex-math id="M7">\begin{document}$\sigma$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M7.png"/></alternatives></inline-formula>, the peak gradually shifts to the right. Conversely, as the noise intensity <inline-formula><tex-math id="M8">\begin{document}$\sigma$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M8.png"/></alternatives></inline-formula> increases, the resonance peak of the coupling strength <inline-formula><tex-math id="M9">\begin{document}$\varepsilon$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210157_M9.png"/></alternatives></inline-formula> and the system size N will also shift to the right.

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“…Tessone et al showed that different sources of diversity can induce a resonant collective behavior in an ensemble of coupled bistable systems and that the systems' response can be optimized by certain value of diversity [12]. Yu et al explored the resonance behavior in two coupled harmonic oscillators and observed that adjusting the coupling strength can not only magnify the SR, but also enrich the resonance forms [44]. Pikovsky demonstrated the existence of system size resonance in different types of coupled stochastic systems [15].…”

Section: Introductionmentioning

confidence: 99%

Collective behaviors of two coupled harmonic oscillators driven by different frequency fluctuations with fractional damping

Jiang¹,

Li²,

Yu³

et al. 2021

J. Stat. Mech.

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In a complex environment, the long-time memory and coupling effect are two important system characteristics that can be described by the fractional damping force and coupling force. This paper investigates the collective behaviors of two coupled fractional harmonic oscillators driven by different frequency fluctuations, including stability, synchronization and stochastic resonance (SR). Theoretically, the ‘synchronization condition’ and ‘stability condition’ of the system are derived. Comparative analysis shows that the latter is stricter than the former. Based on this, an analytical expression of the output amplitude gain is obtained. The numerical results show that when the stability condition is met, the average trajectories of two particles are both bounded and synchronous. Otherwise, they will diverge to infinity. Increasing ɛ (coupling strength) and decreasing α (fractional order) can both accelerate the synchronization speed. SR mainly occurs in the high-α or high-σ (noise amplitude) region, which means that SR emergence can be controlled by adjusting α or σ. The damping force, coupling force and frequency fluctuations compete with each other; thus, the SR intensity should be maximized by adjusting α, ɛ and σ simultaneously.

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The resonance behavior in two coupled harmonic oscillators with fluctuating mass

Cited by 19 publications

References 43 publications

A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

Collective behaviors of globally coupled harmonic oscillators driven by different frequency fluctuations

Collective behaviors of two coupled harmonic oscillators driven by different frequency fluctuations with fractional damping

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